Chapter 11

An object that hangs from the ceiling of a stationary elevator by an ideal spring oscillates with a period T. If the elevator accelerates upward with acceleration 2g, what will be the period of oscillation of the object?

T

Two simple pendulums, A and B, are each 3.0 m long, and the period of pendulum A is T. Pendulum A is twice as heavy as pendulum B. What is the period of pendulum B?

T

The total mechanical energy of a simple harmonic oscillating system is

a non-zero constant.

An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its kinetic energy is a minimum?

at either A or B

A simple harmonic oscillator oscillates with frequency f when its amplitude is A. If the amplitude is now doubled to 2A, what is the new frequency?

f

If the amplitude of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change?

2

If the frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change?

2

If the angular frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum acceleration of the oscillator change?

4

If a string fixed at both ends resonates in its fundamental mode with a frequency of 150 Hz, at which of the following frequencies will it not resonate? (There could be more than one correct choice.)

A) 75 Hz B) 500 Hz

A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now moves downward at a uniform 2 m/s, what is true about the periods of these two systems?

A) Both periods would remain the same.

A mass on a spring undergoes SHM. When the mass passes through the equilibrium position, which of the following statements about it are true? (There could be more than one correct choice.)

A) Its kinetic energy is a maximum. B) Its acceleration is zero. E) Its elastic potential energy is zero.

A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves upward with constant velocity?

A) The period does not change.

If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one correct choice.)

A) The period is reduced to one-half of what it was. D) The angular frequency is doubled.

Why does the intensity of waves from a small source decrease with the square of the distance from the source?

A) The waves spread out as they travel.

An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its kinetic energy is a maximum?

A) midway between A and B

If a guitar string has a fundamental frequency of 500 Hz, which one of the following frequencies can set the string into resonant vibration?

B) 1500 Hz

Four waves are described by the following equations, where distances are measured in meters and times in seconds. I. y = 0.12 cos(3x - 21t) II. y = 0.15 sin(6x + 42t) III. y = 0.13 cos(6x + 21t) IV. y = -0.23 sin(3x - 42t) Which of these waves have the same period?

B) I and III, and also II and IV

Identical balls oscillate with the same period T on Earth. Ball A is attached to an ideal spring and ball B swings back and forth to form a simple pendulum. These systems are now taken to the Moon, where g = 1.6 m/s2, and set into oscillation. Which of the following statements about these systems are true? (There could be more than one correct choice.)

B) On the Moon, ball B will take longer to complete one cycle than ball A. D) On the Moon, ball A will execute more vibrations each minute than ball B.

Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs slow. Which of the following adjustments of the weight would make it more accurate? (There could be more than one correct choice.)

B) Raise the weight.

The intensity of the waves from a point source at a distance d from the source is I. At what distance from the sources is the intensity equal to 2I?

B) d/

In simple harmonic motion, when is the magnitude of the acceleration the greatest? (There could be more than one correct choice.)

B) when the magnitude of the displacement is a maximum C) when the kinetic energy is a minimum D) when the potential energy is a maximum

In simple harmonic motion, when is the speed the greatest? (There could be more than one correct choice.)

B) when the potential energy is a zero D) when the magnitude of the acceleration is a minimum

The intensity of the waves from a point source at a distance d from the source is I. What is the intensity at a distance 2d from the source?

C) I/4

A mass on a spring undergoes SHM. When the mass is at its maximum distance from the equilibrium position, which of the following statements about it are true? (There could be more than one correct choice.)

C) Its speed is zero.

Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs fast. Which of the following adjustments of the weight would make it more accurate? (There could be more than one correct choice.)

C) Lower the weight.

When a guitar is tuned to adjust it pitch, what is it that is changed?

C) The frequency of the fundamental

A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now accelerates downward uniformly at 2 m/s2, what is true about the periods of these two systems?

C) The period of the pendulum would increase but the period of the spring would stay the same.

An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its elastic potential energy is a maximum?

C) at either A or B

An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its elastic potential energy is a minimum?

C) midway between A and B

Four waves are described by the following equations, where distances are measured in meters and times in seconds. I. y = 0.12 cos(3x - 21t) II. y = 0.15 sin(6x + 42t) III. y = 0.13 cos(6x + 21t) IV. y = -0.23 sin(3x - 42t) Which of these waves have the same speed?

D) I and II

A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How would the period of the pendulum change if the supporting chain were to break, putting the elevator into freefall?

D) The period becomes infinite because the pendulum would not swing.

A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves upward with constant acceleration?

D) The period decreases.

A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves downward with constant acceleration?

D) The period increases.

A string of mass m is under tension, and the speed of a wave in the string is v. What will be the speed of a wave in the string if the mass of the string is increased to 2m but with no change in the length or tension?

D)0.71v

A string fixed at both ends is vibrating in one of its harmonics. If we now increase only the frequency at which the string is vibrating, which of the following characteristics do we also increase? (There could be more than one correct choice.)

E) none of the above

An object attached to an ideal spring executes simple harmonic motion. If you want to double its total energy, you could

double the force constant (spring constant) of the spring.

A string of length L is under tension, and the speed of a wave in the string is v. What will be the speed of a wave in the string if the length is increased to 2L but with no change in the mass or tension?

v

When a certain string is under tension T, the speed of a wave in the string is v. What will be the speed of a wave in the string if the tension is increased to 2T without changing the mass or length of the string?

v